The problem with the 3x approximation is that other expenses don't really scale with rent. If you spend $1000/month on food and $2000/month on rent, and then move to a $3000/month apartment, your food cost isn't going to change to $1500. Sure, the local grocery stores and restaurants might be a little more expensive, but not much.

And $1000/m for food is actually really high. That's if you eat lunch and dinner at restaurants every day and don't worry about the price. Figure $500 for food, $500 for health insurance, $150 for transit... it's not adding up to twice rent.